Scientific Performance Audit and Convergence Metrics
This report serves as the official scientific audit for MoeaBench v0.8.0. The objective is to validate and calibrate the numerical integrity and topological fidelity of the framework's core algorithms against established mathematical benchmarks (Ground Truth).
N=200.1000 generations.M=3 objectives for volumetric analysis.EMD < 0.1 represents high-fidelity recovery of the manifold.| Algorithm | IGD (Mean ± Std) | GD (Mean ± Std) | SP (Mean ± Std) | EMD (Wasserstein) | H_raw | H_ratio | H_rel | Time(s) | Stabil. |
|---|---|---|---|---|---|---|---|---|---|
| MOEAD | 0.3076 (Eff: 22.02x) | 3.1689e-01 ± 1.4e+00 | 1.6218e-02 ± 9.9e-03 | 0.0585 (Eff: 6.50x) | 1.3185 | 0.9906 | 99.09% | 117.98 | Gen 500 |
| NSGA2 | 0.0493 (Eff: 3.53x) | 2.4803e-01 ± 1.5e+00 | 4.3729e-02 ± 2.3e-01 | 0.0547 (Eff: 6.08x) | 1.3310 | 1.0000 | 100.02% | 87.18 | Gen 300 |
| NSGA3 | 0.0298 (Eff: 2.13x) | 1.4113e-02 ± 2.0e-03 | 2.7772e-03 ± 9.2e-03 | 0.0543 (Eff: 6.03x) | 1.2642 | 0.9498 | 99.73% | 13.09 | Gen 200 |
| Algorithm | Geometry Status | EXPLORATORY | INDUSTRY | STANDARD | RESEARCH |
|---|---|---|---|---|---|
| MOEAD | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA2 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA3 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| Algorithm | IGD (Mean ± Std) | GD (Mean ± Std) | SP (Mean ± Std) | EMD (Wasserstein) | H_raw | H_ratio | H_rel | Time(s) | Stabil. |
|---|---|---|---|---|---|---|---|---|---|
| MOEAD | 0.0394 (Eff: 1.04x) | 1.8089e-02 ± 8.2e-04 | 8.2981e-03 ± 8.8e-03 | 0.0991 (Eff: 5.24x) | 0.7739 | 0.5815 | 97.11% | 118.74 | Gen 100 |
| NSGA2 | 0.0312 (Eff: 0.82x) | 1.8039e-02 ± 8.3e-04 | 1.6873e-02 ± 9.1e-03 | 0.0828 (Eff: 4.38x) | 0.8311 | 0.6244 | 97.46% | 80.07 | Gen 100 |
| NSGA3 | 0.0398 (Eff: 1.05x) | 1.6911e-02 ± 1.4e-04 | 7.1919e-03 ± 8.7e-03 | 0.0991 (Eff: 5.23x) | 0.7663 | 0.5757 | 96.90% | 13.27 | Gen 100 |
| Algorithm | Geometry Status | EXPLORATORY | INDUSTRY | STANDARD | RESEARCH |
|---|---|---|---|---|---|
| MOEAD | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA2 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA3 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| Algorithm | IGD (Mean ± Std) | GD (Mean ± Std) | SP (Mean ± Std) | EMD (Wasserstein) | H_raw | H_ratio | H_rel | Time(s) | Stabil. |
|---|---|---|---|---|---|---|---|---|---|
| MOEAD | 0.5402 (Eff: 14.20x) | 1.6522e+00 ± 1.1e+00 | 2.1422e-01 ± 2.8e-02 | 0.3004 (Eff: 15.49x) | 1.2829 | 0.9639 | 96.56% | 112.82 | Gen 1000 |
| NSGA2 | 0.5989 (Eff: 15.75x) | 2.3090e+00 ± 1.4e+01 | 1.5829e-01 ± 8.7e-01 | 0.0976 (Eff: 5.03x) | 1.3310 | 1.0000 | 100.00% | 84.55 | Gen 400 |
| NSGA3 | 0.4198 (Eff: 11.04x) | 5.4060e-01 ± 1.7e+00 | 1.6181e-01 ± 5.1e-01 | 0.1087 (Eff: 5.61x) | 1.3309 | 0.9999 | 99.99% | 12.43 | Gen 600 |
| Algorithm | Geometry Status | EXPLORATORY | INDUSTRY | STANDARD | RESEARCH |
|---|---|---|---|---|---|
| MOEAD | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA2 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA3 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| Algorithm | IGD (Mean ± Std) | GD (Mean ± Std) | SP (Mean ± Std) | EMD (Wasserstein) | H_raw | H_ratio | H_rel | Time(s) | Stabil. |
|---|---|---|---|---|---|---|---|---|---|
| MOEAD | 0.0349 (Eff: 0.92x) | 1.8882e-02 ± 1.3e-03 | 1.3461e-02 ± 7.7e-03 | 0.2163 (Eff: 10.22x) | 0.7705 | 0.5789 | 97.98% | 112.80 | Gen 100 |
| NSGA2 | 0.0326 (Eff: 0.86x) | 1.7482e-02 ± 6.3e-04 | 1.8044e-02 ± 8.7e-03 | 0.1038 (Eff: 4.91x) | 0.8314 | 0.6247 | 97.26% | 77.83 | Gen 100 |
| NSGA3 | 0.0398 (Eff: 1.05x) | 1.6920e-02 ± 4.3e-04 | 7.2102e-03 ± 8.7e-03 | 0.1085 (Eff: 5.13x) | 0.7718 | 0.5799 | 97.06% | 12.55 | Gen 100 |
| Algorithm | Geometry Status | EXPLORATORY | INDUSTRY | STANDARD | RESEARCH |
|---|---|---|---|---|---|
| MOEAD | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA2 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA3 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| Algorithm | IGD (Mean ± Std) | GD (Mean ± Std) | SP (Mean ± Std) | EMD (Wasserstein) | H_raw | H_ratio | H_rel | Time(s) | Stabil. |
|---|---|---|---|---|---|---|---|---|---|
| MOEAD | 0.0068 (Eff: 2.11x) | 6.5874e-04 ± 3.8e-04 | 5.2277e-03 ± 8.3e-03 | 0.2260 (Eff: 18.29x) | 0.4206 | 0.3160 | 98.91% | 111.16 | Gen 100 |
| NSGA2 | 0.0019 (Eff: 0.59x) | 7.9038e-04 ± 1.9e-04 | 1.7806e-03 ± 1.3e-03 | 0.0271 (Eff: 2.19x) | 0.2691 | 0.2022 | 99.65% | 82.41 | Gen 300 |
| NSGA3 | 0.0038 (Eff: 1.19x) | 4.9039e-04 ± 3.3e-05 | 2.6192e-03 ± 2.2e-03 | 0.0951 (Eff: 7.69x) | 0.2692 | 0.2023 | 99.16% | 11.83 | Gen 100 |
| Algorithm | Geometry Status | EXPLORATORY | INDUSTRY | STANDARD | RESEARCH |
|---|---|---|---|---|---|
| MOEAD | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA2 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA3 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| Algorithm | IGD (Mean ± Std) | GD (Mean ± Std) | SP (Mean ± Std) | EMD (Wasserstein) | H_raw | H_ratio | H_rel | Time(s) | Stabil. |
|---|---|---|---|---|---|---|---|---|---|
| MOEAD | 0.0560 (Eff: 17.41x) | 8.9077e-02 ± 2.6e-02 | 1.5905e-02 ± 1.2e-02 | 0.2369 (Eff: 17.85x) | 0.6251 | 0.4696 | 93.81% | 112.39 | Gen 200 |
| NSGA2 | 0.1586 (Eff: 49.34x) | 2.0389e-01 ± 5.9e-01 | 1.0132e-02 ± 1.7e-02 | 0.0569 (Eff: 4.29x) | 1.2665 | 0.9516 | 99.07% | 76.78 | Gen 400 |
| NSGA3 | 0.1930 (Eff: 60.05x) | 2.4915e-01 ± 6.0e-01 | 1.6877e-02 ± 1.8e-02 | 0.1609 (Eff: 12.12x) | 1.2459 | 0.9360 | 98.39% | 14.64 | Gen 600 |
| Algorithm | Geometry Status | EXPLORATORY | INDUSTRY | STANDARD | RESEARCH |
|---|---|---|---|---|---|
| MOEAD | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA2 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA3 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| Algorithm | IGD (Mean ± Std) | GD (Mean ± Std) | SP (Mean ± Std) | EMD (Wasserstein) | H_raw | H_ratio | H_rel | Time(s) | Stabil. |
|---|---|---|---|---|---|---|---|---|---|
| MOEAD | 0.0928 (Eff: 2.99x) | 2.2038e-02 ± 1.7e-03 | 0.0000e+00 ± 0.0e+00 | 0.5379 (Eff: 21.65x) | 0.0000 | 0.0000 | 0.00% | 10.00 | Gen 200 |
| NSGA2 | 0.0340 (Eff: 1.09x) | 2.0875e-02 ± 3.9e-03 | 3.4321e-02 ± 4.3e-03 | 0.0769 (Eff: 3.10x) | 0.6885 | 0.5173 | 96.53% | 76.05 | Gen 200 |
| NSGA3 | 0.1128 (Eff: 3.63x) | 2.2767e-02 ± 6.6e-03 | 0.0000e+00 ± 0.0e+00 | 0.0743 (Eff: 2.99x) | 0.0000 | 0.0000 | 0.00% | 10.00 | Gen 300 |
| Algorithm | Geometry Status | EXPLORATORY | INDUSTRY | STANDARD | RESEARCH |
|---|---|---|---|---|---|
| MOEAD | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA2 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA3 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| Algorithm | IGD (Mean ± Std) | GD (Mean ± Std) | SP (Mean ± Std) | EMD (Wasserstein) | H_raw | H_ratio | H_rel | Time(s) | Stabil. |
|---|---|---|---|---|---|---|---|---|---|
| NSGA2 | 840.6049 (Eff: 30620.57x) | 8.4035e+02 ± 1.0e+03 | 1.1544e-03 ± 2.2e-03 | 0.2982 (Eff: 20.23x) | 0.7990 | 0.6003 | 60.03% | 30.89 | Gen 500 |
| NSGA3 | 0.0490 (Eff: 1.79x) | 1.6853e-02 ± 9.9e-04 | 1.7490e-02 ± 1.7e-03 | 0.0187 (Eff: 1.27x) | 0.9724 | 0.7306 | 94.99% | 15.26 | Gen 500 |
| Algorithm | Geometry Status | EXPLORATORY | INDUSTRY | STANDARD | RESEARCH |
|---|---|---|---|---|---|
| NSGA2 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA3 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| Algorithm | IGD (Mean ± Std) | GD (Mean ± Std) | SP (Mean ± Std) | EMD (Wasserstein) | H_raw | H_ratio | H_rel | Time(s) | Stabil. |
|---|---|---|---|---|---|---|---|---|---|
| NSGA2 | 1730.8555 (Eff: 439604.50x) | 1.7308e+03 ± 0.0e+00 | 0.0000e+00 ± 0.0e+00 | 999.3098 (Eff: 67111.57x) | 0.0010 | 0.0008 | 0.08% | 12.75 | Gen 100 |
| NSGA3 | 0.2067 (Eff: 52.50x) | 6.6958e-02 ± 6.7e-03 | 8.3061e-03 ± 1.0e-03 | 0.2184 (Eff: 14.67x) | 0.1461 | 0.1098 | 54.21% | 15.08 | Gen 500 |
| Algorithm | Geometry Status | EXPLORATORY | INDUSTRY | STANDARD | RESEARCH |
|---|---|---|---|---|---|
| NSGA2 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA3 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| Algorithm | IGD (Mean ± Std) | GD (Mean ± Std) | SP (Mean ± Std) | EMD (Wasserstein) | H_raw | H_ratio | H_rel | Time(s) | Stabil. |
|---|---|---|---|---|---|---|---|---|---|
| MOEAD | 0.3479 (Eff: 204.64x) | 3.1650e-01 ± 9.8e-01 | 5.1073e-03 ± 2.4e-03 | 0.0606 (Eff: 9.58x) | 1.2175 | 0.9147 | 94.40% | 117.58 | Gen 500 |
| NSGA2 | 0.0051 (Eff: 2.99x) | 2.3259e-02 ± 1.4e-01 | 1.3109e-03 ± 3.0e-03 | 0.0043 (Eff: 0.67x) | 1.1720 | 0.8805 | 99.83% | 82.37 | Gen 400 |
| NSGA3 | 0.0937 (Eff: 55.14x) | 9.7682e-02 ± 4.5e-01 | 1.6700e-03 ± 1.3e-03 | 0.0421 (Eff: 6.66x) | 1.2042 | 0.9048 | 97.41% | 12.23 | Gen 400 |
| Algorithm | Geometry Status | EXPLORATORY | INDUSTRY | STANDARD | RESEARCH |
|---|---|---|---|---|---|
| MOEAD | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA2 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA3 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| Algorithm | IGD (Mean ± Std) | GD (Mean ± Std) | SP (Mean ± Std) | EMD (Wasserstein) | H_raw | H_ratio | H_rel | Time(s) | Stabil. |
|---|---|---|---|---|---|---|---|---|---|
| MOEAD | 0.9019 (Eff: 55.00x) | 4.0960e-05 ± 4.5e-07 | 3.5453e-03 ± 8.4e-06 | 1.7520 (Eff: 35.05x) | 0.1921 | 0.1443 | 49.90% | 115.59 | Gen 100 |
| NSGA2 | 0.0017 (Eff: 0.11x) | 1.2828e-04 ± 2.0e-05 | 1.0080e-02 ± 8.1e-03 | 0.2300 (Eff: 4.60x) | 0.3841 | 0.2886 | 99.72% | 72.52 | Gen 100 |
| NSGA3 | 0.0031 (Eff: 0.19x) | 1.2220e-04 ± 1.5e-05 | 1.4596e-02 ± 1.2e-02 | 0.5447 (Eff: 10.90x) | 0.3844 | 0.2888 | 99.54% | 13.38 | Gen 200 |
| Algorithm | Geometry Status | EXPLORATORY | INDUSTRY | STANDARD | RESEARCH |
|---|---|---|---|---|---|
| MOEAD | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA2 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA3 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| Algorithm | IGD (Mean ± Std) | GD (Mean ± Std) | SP (Mean ± Std) | EMD (Wasserstein) | H_raw | H_ratio | H_rel | Time(s) | Stabil. |
|---|---|---|---|---|---|---|---|---|---|
| NSGA2 | 0.0016 (Eff: 0.58x) | 3.0564e-03 ± 1.2e-04 | 2.0067e-03 ± 1.4e-03 | 0.2914 (Eff: 55.12x) | 0.7945 | 0.5969 | 100.22% | 75.93 | Gen 800 |
| NSGA3 | 0.0042 (Eff: 1.54x) | 3.1938e-03 ± 1.6e-04 | 3.0014e-03 ± 2.3e-03 | 0.3242 (Eff: 61.32x) | 0.7982 | 0.5997 | 99.99% | 12.23 | Gen 100 |
| Algorithm | Geometry Status | EXPLORATORY | INDUSTRY | STANDARD | RESEARCH |
|---|---|---|---|---|---|
| NSGA2 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA3 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| Algorithm | IGD (Mean ± Std) | GD (Mean ± Std) | SP (Mean ± Std) | EMD (Wasserstein) | H_raw | H_ratio | H_rel | Time(s) | Stabil. |
|---|---|---|---|---|---|---|---|---|---|
| MOEAD | 0.5025 (Eff: 120.58x) | 1.4101e-01 ± 7.8e-01 | 8.9064e-04 ± 1.6e-03 | 0.1243 (Eff: 11.41x) | 0.6949 | 0.5221 | 53.27% | 121.37 | Gen 300 |
| NSGA2 | 0.0044 (Eff: 1.05x) | 2.4544e-02 ± 1.5e-01 | 3.3861e-03 ± 3.4e-03 | 0.0142 (Eff: 1.31x) | 1.1632 | 0.8739 | 99.64% | 82.92 | Gen 200 |
| NSGA3 | 0.0233 (Eff: 5.59x) | 1.8991e-02 ± 1.2e-01 | 1.3051e-02 ± 4.9e-02 | 0.0426 (Eff: 3.91x) | 1.3061 | 0.9813 | 99.68% | 12.23 | Gen 200 |
| Algorithm | Geometry Status | EXPLORATORY | INDUSTRY | STANDARD | RESEARCH |
|---|---|---|---|---|---|
| MOEAD | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA2 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA3 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| Algorithm | IGD (Mean ± Std) | GD (Mean ± Std) | SP (Mean ± Std) | EMD (Wasserstein) | H_raw | H_ratio | H_rel | Time(s) | Stabil. |
|---|---|---|---|---|---|---|---|---|---|
| MOEAD | 0.0304 (Eff: 1.60x) | 6.7792e-03 ± 1.4e-04 | 1.6212e-02 ± 2.0e-02 | 0.1130 (Eff: 5.93x) | 0.7066 | 0.5309 | 96.80% | 113.39 | Gen 100 |
| NSGA2 | 0.0142 (Eff: 0.75x) | 9.1868e-03 ± 4.9e-03 | 2.0535e-02 ± 8.9e-03 | 0.1023 (Eff: 5.38x) | 1.1082 | 0.8326 | 99.13% | 81.79 | Gen 100 |
| NSGA3 | 0.0239 (Eff: 1.26x) | 6.2888e-03 ± 1.8e-04 | 1.8744e-02 ± 1.0e-02 | 0.2093 (Eff: 11.00x) | 0.7885 | 0.5924 | 97.87% | 12.51 | Gen 200 |
| Algorithm | Geometry Status | EXPLORATORY | INDUSTRY | STANDARD | RESEARCH |
|---|---|---|---|---|---|
| MOEAD | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA2 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |
| NSGA3 | IDEAL_FRONT Ideal Front. Excellent convergence, purity, and topology. | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x | PASS IGD_eff=1.00x, EMD_eff=0.00x |